In the standard 243 Win the Barnes web site says H4350 is their most accurate powder also showing fastest velocity w/45.5 max load at 3398fps.
I shoot a 243AI custom and usually 2-3 grain of powder over max for standard case is max for the AI as rule of thumb.
With the 85 grain bullets the 4350 powders gave me the best results in my standard 243. I only shoot the heavy's in my AI. If I was to shoot the 80-85's in the AI would definitely try shooting 4350.
In 2 other rifle that I shoot the Barnes TTSX in I have found the Barnes loads to be quite accurate.